论文标题
通过随机屏蔽解决离子通道噪声对串联间隔变化的分子贡献
Resolving Molecular Contributions of Ion Channel Noise to Interspike Interval Variability through Stochastic Shielding
论文作者
论文摘要
以前在基于电导率的模型离子状态图内,独立噪声源对动作电势时机变异性的贡献尚未在单个定向分子过渡的水平上进行了研究。基本联系提供了一个重要的例子,说明了如何应用数学来研究不可观察的显微镜波动对宏观可观察到的数量的影响。我们研究了随机的langevin模型,并展示了如何解决离子通道图中每个过渡对串联间隔(ISI)方差的单个贡献。我们将在(Cao等,2020,Siam J.Appl。Math)中开发的平均值 - 返回时间(MRT)阶段还原扩展到从MRT等位置体到自身的返回时间的第二刻。由于固定电压尖峰检测触发器不对应于MRT等位线,因此相相间隔(IPI)方差仅近似ISI方差。我们发现,当两者都可以计算时,IPI差异和ISI方差同意在几%之内。此外,我们严格地证明,并在数值上表明,我们对IPI方差的表达在小噪声(较大的系统大小)制度中是准确的。我们的理论是小噪声的极限。通过选择性地包括仅与大多数ISI方差的少数过渡相关的噪声,我们的分析将随机屏蔽(SS)范式扩展到从固定电压夹具案例的范围(Schmandt等,Phys。Phys。Rev。the Rev.)。我们从数值上表明,即使对于较大的生理相关噪声水平,SS近似也具有高度的精度。我们表明,ISI方差不是明确定义的数量,而是取决于在体外和计算机中将电压水平设置为尖峰检测阈值的选择。
The contributions of independent noise sources to the variability of action potential timing has not previously been studied at the level of individual directed molecular transitions within a conductance-based model ion-state graph. The underlying connection provides an important example of how mathematics can be applied to study the effects of unobservable microscopic fluctuations to macroscopically observable quantities. We study a stochastic Langevin model and show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean--return-time (MRT) phase reduction developed in (Cao et al. 2020, SIAM J. Appl. Math) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike-detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt et al. 2012, Phys. Rev. Lett.) from the stationary voltage-clamp case to the current-clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. We show that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike-detection threshold, both in vitro and in silico.